Soccer balls, golf balls, and the Euler identity. (English) Zbl 1391.05247

Summary: We show, with simple combinatorics, that if the dimples on a golf ball are all 5-sided and 6-sided polygons, with three dimples at each “vertex”, then no matter how many dimples there are and no matter the sizes and distribution of the dimples, there will always be exactly twelve 5-sided dimples. Of course, the same is true of a soccer ball and its faces.


05C99 Graph theory
Full Text: Euclid


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